Math Chapter 3 project

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Spokane Falls Community College *

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146

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Mathematics

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Feb 20, 2024

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pdf

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Ron Varner Math 146 Professor Wildman 02/08//2024 Chapter 3 Project - Exploratory data analysis: Problem #1: #1) Mean = 7.03, Median = 7, Mode = 3, Standard deviation = 4.38, Range = 15, Five number summary = 0, 3, 7, 11, 15 #2) Stacked box plot with grams of sugar per seving and shelf level.
#3) Mean = 2.51, Median = 2.5, Mode = 3, Standard deviation = 1.06, Range = 5, Five Number Summary = 1, 2, 2.5, 3, 6 #4) Cereals with the highest sugar content are indeed placed at kid-eye level. In this example it would be the middle-shelf. This correlation between the eye-level shelf and the highest sugar content within the cereals becomes abundantly clear when we compare the mean, median, mode, Standard deviation, and range of all the cereals compared to the middle-shelf. The middle-shelf cereals had a “greater than'' sugar content in every part of the data summary. For example the middle shelves cereal averages 9.62 grams of sugar per serving, on the other hand the average amount of grams of sugar per serving in all the cereals was only 7.03. Another good indication is the median for the middle shelf is 12 grams of sugar per serving whilst all the cereals had a median of 7 grams of sugar per serving. Additionally, the mode for the middle-shelf is much larger sitting at 12 grams of sugar per serving compared to all the cereals mode which was 3 grams of sugar per serving. As well as that, to further back up this conclusion we can see on our box plot that Q1 of the middle-shelf is higher than Q2 of both shelf 1 and 2. This ultimately means that 75% of the middle-shelves cereals have a higher sugar content then 50% of the cereals on the all shelfs. Another way of looking at Q1 of the middle-shelf being higher than Q2 of the all shelfs is that the lower 25% of the middle-shelf is higher than the median value for the all the shelfs. All of these values being larger in sugar content compared to the sugar content of all the cereals indicates that a large portion of the sugary cereals are placed at kid-eye level.
#4b) Cereals with the least protein in grams per serving are commonly found at the kid-eye level middle-shelf. This can clearly be seen when we compare the data summary of the grams of protein per serving of the middle-shelves cereals compared to the average of all the shelfs cereals. Right away you will notice that all the values in the data summary for the middle-shelf are all lower than the values for all the cereals. For example the average protein in grams per serving found on the middle shelf is 1.9g, in comparison to all the cereals average of 2.51g protein. Additionally, the median for the middle-shelf is 2g compared to the median of all the cereals at 2.5g. Not surprisingly the mode is also lower sitting right at 1g protein per serving, compared to the 3g protein per serving for all the cereals. Furthermore, the middle-shelf has a protein range of only 1-3g, while all of the cereals range from 1-5 grams protein. Not only this, but also Q3 of the middle-shelf is equal to Q1 for the other two shelves, this indicates that 75% of the middle-shelves cereals are lower in grams protein per serving than the 25th percentile of the other two shelves cereals. Problem #2: Cookie Data) 7.5cm, 24g, 13cc, 4 taste 6.5cm, 17g, 10cc, 4 taste 9.5cm, 37g, 12cc, 4 taste 6.25cm, 17g, 8cc, 3 taste 6cm, 16g, 9cc, 2 taste 7.5cm, 20g, 6cc, 2 taste #1) Weight - mean 21.28, median 20, mode 24, Standard deviation 7.00, range 30, 5# summary 10, 16.5, 20, 24.5, 40 Diameter - mean 7.16, median 7.5, mode 7.5, standard deviation 1.18, range 4.5, 5# summary 5, 6.125, 7.5, 8, 9.5 Chocolate Chips - mean 11.08, median 10.5, mode 9, standard deviation 4.29, range 17, 5# summary 4, 8.5, 10.5, 14.5, 21 #2) boxplot showing outliers
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